# Wave Energy Formula

You may have been near to any seashore if you stay close to such places. When the wind passes on the water surface, it leads to the pressure difference between the upper and bottom wind that results in the generation of waves. Wave energy is the energy that is gained by the waves. When the wind blows on the seashore, it shifts its energy to these waves. These waves carry a lot of power which we call wave power.

## Formula of Wave Energy

The wave energy density formula according to linear wave theory is

$E=\rho gH^{^{2}}/16$

Where,

• E is the mean wave energy density
• H is the wave height
• ρ is the water density
• g is the acceleration due to gravity

The wave power formula in terms of wave energy is given by,

$P = E_{cg}$

Where,

• cg is the group velocity in m/s.

### Solved Numericals

Example 1

A wave in a seashore travels with a height of 5 m. Determine the wave energy density.

Solution:

Given:

$E=\rho gH^{^{2}}/16$

Wave height H = 5 m,

Water density ρ = 999.97 kg/m3,

Gravity g = 9.8 m/s2

The wave energy formula is given by,

E = 999.97 × 9.8 × 25 / 16

E = 15312 J

Example 2

A huge wave travels with the energy of 8000 J. Determine its wave height.

Solution:

Given:

Wave energy E = 8000J,

Water density ρ = 999.97 kg/m3,

Gravity g = 9.8 m/s2

The wave height is calculated by wave energy formula,

H = √16E / ρg

= √16 x 8000 /(999.97 x 9.8)

H = 357.7/9799.70

The wave height of the wave is 0.0365 m

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